General scalar renormalisation group equations at three-loop order

• DOI: 10.1007/jhep12(2020)012
• Publication Date: 2020-12-10T07:03:04Z
• Authors: Tom Steudtner
• Keywords: High Energy Physics - Theory; High Energy Physics - Phenomenology; High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; FOS: Physical sciences; Renormalization Group; Renormalization Regularization and Renormalons; QC770-798; 01 natural sciences

Abstract For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $$ \overline{\mathrm{MS}} $$

MS ¯

scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and from those derive β functions for scalar masses and cubic interactions. As an example, the results are applied to compute all renormalisation group equations in U(n) × U(n) scalar theories.